Will I lose my work if I update from Free version to Pro version?

No, you will not lose the changes that you have made in your free theme when you Upgrade to Pro theme. All your content, theme settings should remain as it is even after switching/upgrading to Pro theme.

You can simply install the Pro version, activate it and enjoy the added features and flexibility.

However there is nothing wrong on creating backup of your site.

Note: If you have made changes directly on the theme code file(Hope you have not), then those changes will get lost when you upgrade the theme. Hence it is never recommended to make code changes directly on theme file. Always create child theme and proceed if you want to make code changes.